Exact stability analysis of 2D systems using LMIs
Yoshio Ebihara, Y. Ito, T. Hagiwara · 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601) · 2004
In this paper, we propose necessary and sufficient conditions for asymptotic stability analysis of 2D systems in terms linear matrix inequalities (LMIs). By introducing a guardian map for the set of Schur stable complex matrices, we first reduce the stability analysis problems into nonsingularity analysis problems of parameter-dependent complex matrices. Then, by means of the discrete-time positive real lemma and the generalized S-procedure, we derive LMI-based conditions to verify the asymptotic stability in an exact (i.e., nonconservative) fashion. It turns out that we can reduce the size of LMIs by employing the generalized S-procedure.